@Article{Lapa2023,
author = "Lapa, Eugenio Cabanillas",
title = "Global solutions for a nonlinear Kirchhoff type equation with viscosity",
journal = "Opuscula Math.",
year = "2023",
volume = "43",
number = "5",
pages = "689--701",
doi = "https://doi.org/10.7494/OpMath.2023.43.5.689",
url = "https://doi.org/10.7494/OpMath.2023.43.5.689",
abstract = "In this paper we consider the existence and asymptotic behavior of solutions of the following nonlinear Kirchhoff type problem \[u_{tt}- M\left(\,\displaystyle \int_{\Omega}|\nabla u|^{2}\, dx\right)\triangle u - \delta\triangle u_{t}= \mu|u|^{\rho-2}u\quad \text{in } \Omega \times ]0,\infty[,\] where \[M(s)=\begin{cases}a-bs &\text{for } s \in [0,\frac{a}{b}[,\\ 0, &\text{for } s \in [\frac{a}{b}, +\infty[.\end{cases}\] If the initial energy is appropriately small, we derive the global existence theorem and its exponential decay.",
keywords = "global solutions, nonlinear Kirchhoff type problem, exponential decay",
issn = "1232-9274"
}